Let G =
(V(G),E(G))
be a simple undirected graph. The reinforcement number of a graph is a vulnerability
parameter of a graph. We have investigated a refinement that involves the average lower
reinforcement number of this parameter. The lower reinforcement number,
denoted by re∗(G),
is the minimum cardinality of reinforcement set in G that contains the edge
e∗ of the complement graph G̅
. The average lower reinforcement number
of G
is defined by
rav(G)=1/|E(G̅)| ∑e** ∈ E(G̅)re*(G)
.In this paper, we define the average lower
reinforcement number of a graph and we present the exact values for some
well−known graph families.